"It's really cool to get a chance to do this," Baker said. "I was having trouble not smiling on the mound. You never get opportunities to do things like this."
The 33-year-old Baker joked that he might not have pitched since he was college-aged.
"It was the Cape Cod League," he said. "I believe I had like a 27.00 ERA, but I was getting squeezed from what I remember."
Chicago used seven relievers before Baker (1-0) became the first Cubs position player to take the mound since Aug. 27, 2012, when Joe Mather faced Milwaukee.
The Rockies also used all seven relievers in their bullpen, then turned to Tyler Matzek, a starter, in the 16th.
Matzek (2-5) walked Baker to lead off the inning. Baker advanced to second on a sacrifice then to third on Anthony Rizzo's bloop single before scoring.
"I've thrown in the pen before and had a routine down," Matzek said. "So it wasn't anything crazy. I just didn't execute."
Chicago's Emilio Bonifacio had a game-tying two-run homer in the fourth inning and a double among four hits. He is 14 for 35 since returning from the disabled list (strained right oblique) on July 22.
Rockies first baseman Justin Morneau returned from the disabled list and drove in two runs with a double. Corey Dickerson added two hits and an RBI
Morneau, who had been out since July 13 with a strained neck, entered hitting .312, third best in the National League. He leads Colorado with 62 RBIs.
Cubs starter Edwin Jackson lasted just four innings, laboring with 105 pitches and allowing three runs on six hits and three walks.
Jackson allowed all three Colorado runs in the first, then Chicago's bullpen plus Baker held the Rockies scoreless for 15 innings.
"When you go 15 innings without scoring a run, you don't deserve to win," Colorado manager Walt Weiss said.
Both teams had chances to win in the 10th.
Colorado's D.J. LeMahieu missed on a suicide squeeze with Morneau on third and Charlie Culberson on second. Morneau was tagged out by catcher Welington Castillo.
In the bottom of the inning, Castillo lined a drive deep to center field with one out and Castro on second. But the Rockies' Charlie Blackmon raced back and made a spectacular diving catch.